The given expression is equivalent to the expression (B) [tex](x-1)^{2} -3[/tex].
What is an equivalent function?
- Two functions are equivalent if they share the same domain and codomain and have the same values for all domain components.
To complete the square to transform the expression:
- The given expression is [tex]x^{2} -2x-2[/tex].
- Then the expression can be written as, add and subtract one.
- Then we have:
- [tex]x^{2} -2x+1-1-2\\x^{2} -2x+1-3\\(x-1)^{2} -3[/tex]
Therefore, the given expression is equivalent to the expression (B) [tex](x-1)^{2} -3[/tex].
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The correct question is shown below:
Complete the square to transform the expression x^2− 2x − 2 into the form a(x − h)^2+ k.
(A) (x − 1)2 + 3
(B) (x − 1)2 − 3
(C) (x − 2)2 − 3
(D) (x − 2)2 + 3